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Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture

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Arone G., Lesh K.

Fundamenta Mathematicae

2010

tom 207

nr 1

29-70

We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of Rognes by showing that our auxiliary complex can be constructed in terms of the stable rank filtration. As a by-product, we verify for the case of topological complex K-theory a conjecture made by Rognes about the connectivity (for certain rings) of the filtration subquotients of the stable rank filtration of algebraic K-theory.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Arone G.

1 Lesh K.

1 2010

Wyniki wyszukiwania

Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture